Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Tarsi, Cristina"'
\noindent We are concerned with positive normalized solutions $(u,\lambda)\in H^1(\mathbb{R}^2)\times\mathbb{R}$ to the following semi-linear Schr\"{o}dinger equations $$ -\Delta u+\lambda u=f(u), \quad\text{in}~\mathbb{R}^2, $$ satisfying the mass c
Externí odkaz:
http://arxiv.org/abs/2407.10258
We provide an existence result for a Schr\"odinger-Poisson system in gradient form, set in the whole plane, in the case of zero mass. Since the setting is limiting for the Sobolev embedding, we admit nonlinearities with subcritical or critical growth
Externí odkaz:
http://arxiv.org/abs/2405.03871
We consider the semilinear elliptic equations $$ \left\{ \begin{array}{ll} &-\Delta u+V(x)u=\left(I_\alpha\ast |u|^p\right)|u|^{p-2}u+\lambda u\quad \hbox{for } x\in\mathbb R^N, \\ &u(x) \to 0 \hbox{ as } |x| \to\infty, \end{array} \right. $$ where $
Externí odkaz:
http://arxiv.org/abs/2205.02542
We consider the $N$-Laplacian Schr\"odinger equation strongly coupled with higher order fractional Poisson's equations. When the order of the Riesz potential $\alpha$ is equal to the Euclidean dimension $N$, and thus it is a logarithm, the system tur
Externí odkaz:
http://arxiv.org/abs/2201.00159
Autor:
Cassani, Daniele, Tarsi, Cristina
We study the following Choquard type equation in the whole plane $(C) -\Delta u+V(x)u=(I_2\ast F(x,u))f(x,u),x\in\mathbb{R}^2$ where $I_2$ is the Newton logarithmic kernel, $V$ is a bounded Schr\"odinger potential and the nonlinearity $f(x,u)$, whose
Externí odkaz:
http://arxiv.org/abs/2104.04930
Publikováno v:
In Journal of Differential Equations 15 August 2022 328:261-294
We investigate connections between Hardy's inequality in the whole space $\mathbb{R}^n$ and embedding inequalities for Sobolev-Lorentz spaces. In particular, we complete previous results due to [A. Alvino, Sulla diseguaglianza di Sobolev in spazi di
Externí odkaz:
http://arxiv.org/abs/1711.03763
We study the following singularly perturbed nonlocal Schr\"{o}dinger equation $$ -\vr^2\Delta u +V(x)u =\vr^{\mu-2}\Big[\frac{1}{|x|^{\mu}}\ast F(u)\Big]f(u) \quad \mbox{in} \quad \R^2, $$ where $V(x)$ is a continuous real function on $\R^2$, $F(s)$
Externí odkaz:
http://arxiv.org/abs/1601.01743
We first investigate concentration and vanishing phenomena concerning Moser type inequalities in the whole plane which involve complete and reduced Sobolev norms. In particular we show that the critical Ruf inequality is equivalent to an improved ver
Externí odkaz:
http://arxiv.org/abs/1402.2083
Publikováno v:
Communications in Contemporary Mathematics; Apr2024, Vol. 26 Issue 3, p1-35, 35p